9y^2+30y=25

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Solution for 9y^2+30y=25 equation: 


Simplifying
9y2 + 30y = 25

Reorder the terms:
30y + 9y2 = 25

Solving
30y + 9y2 = 25

Solving for variable 'y'.

Reorder the terms:
-25 + 30y + 9y2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 30y + 9y2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-2.777777778 + 3.333333333y + y2 = 0

Move the constant term to the right:

Add '2.777777778' to each side of the equation.
-2.777777778 + 3.333333333y + 2.777777778 + y2 = 0 + 2.777777778

Reorder the terms:
-2.777777778 + 2.777777778 + 3.333333333y + y2 = 0 + 2.777777778

Combine like terms: -2.777777778 + 2.777777778 = 0.000000000
0.000000000 + 3.333333333y + y2 = 0 + 2.777777778
3.333333333y + y2 = 0 + 2.777777778

Combine like terms: 0 + 2.777777778 = 2.777777778
3.333333333y + y2 = 2.777777778

The y term is 3.333333333y.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333y + 2.777777779 + y2 = 2.777777778 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333y + y2 = 2.777777778 + 2.777777779

Combine like terms: 2.777777778 + 2.777777779 = 5.555555557
2.777777779 + 3.333333333y + y2 = 5.555555557

Factor a perfect square on the left side:
(y + 1.666666667)(y + 1.666666667) = 5.555555557

Calculate the square root of the right side: 2.357022604

Break this problem into two subproblems by setting 
(y + 1.666666667) equal to 2.357022604 and -2.357022604.


Subproblem 1
y + 1.666666667 = 2.357022604

Simplifying
y + 1.666666667 = 2.357022604

Reorder the terms:
1.666666667 + y = 2.357022604

Solving
1.666666667 + y = 2.357022604

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + y = 2.357022604 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + y = 2.357022604 + -1.666666667
y = 2.357022604 + -1.666666667

Combine like terms: 2.357022604 + -1.666666667 = 0.690355937
y = 0.690355937

Simplifying
y = 0.690355937


Subproblem 2
y + 1.666666667 = -2.357022604

Simplifying
y + 1.666666667 = -2.357022604

Reorder the terms:
1.666666667 + y = -2.357022604

Solving
1.666666667 + y = -2.357022604

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + y = -2.357022604 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + y = -2.357022604 + -1.666666667
y = -2.357022604 + -1.666666667

Combine like terms: -2.357022604 + -1.666666667 = -4.023689271
y = -4.023689271

Simplifying
y = -4.023689271


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.690355937, -4.023689271}

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